Question

question 16 (1 point)
the co - terminal angles to an angle ( \theta ) may be determined using the expression
( \bigcirc ) a) ( \theta+360^{circ} \times n, n in i )
( \bigcirc ) b) ( \theta+180^{circ} \times n, n in i )
( \bigcirc ) c) ( \theta-360^{circ} \times n, n in mathbb{r} )
( \bigcirc ) d) ( \theta-180^{circ} \times n, n in i )

Explanation:

Step1: Recall the definition of co - terminal angles

Co - terminal angles are angles that have the same initial and terminal sides. When we rotate an angle by a full - circle (either clockwise or counter - clockwise), we get a co - terminal angle. A full - circle rotation is \(360^{\circ}\).

Step2: Analyze the general formula for co - terminal angles

If we start with an angle \(\theta\), and we add or subtract an integer multiple of \(360^{\circ}\), we get a co - terminal angle. The general formula for co - terminal angles is \(\theta + 360^{\circ}\times n\), where \(n\in I\) ( \(I\) represents the set of integers).

• For option b: \(180^{\circ}\) rotation gives angles that are supplementary or form a straight - line relationship (not co - terminal in the general full - circle sense).
• For option c: The set of values for \(n\) should be integers (\(n\in I\)) not real numbers (\(n\in\mathbb{R}\)).
• For option d: Similar to option b, \(180^{\circ}\) rotation does not give co - terminal angles in the standard full - circle definition.

Answer:

A. \(\theta + 360^{\circ}\times n,n\in I\)